I'd prefer an addon (read: full blown addon, no DLCs) over a follow-up. Also, I think a BRINK 2 could only work in a way that Bioshock Infinite works compared to the original Bioshock (remember: Bioshock 2 was not developed by the original team).
I didn't know that Bioshock 2 was a different developer, they really did an impressive job at capturing the atmosphere of the first game.
Without knowing the ending of Brink yet, its hard to say, but it doesn't seem like the story would lend itself to a sequel very well. You have a civil war in the middle of the sea on a floating manmade island. One of the sides of the war is probobally gonna have to win, or there's at least going to have to be a conclusion of some sort. For a sequel you would need to have another war on the Ark, which would be hard to make a storyline for. Unless this game ends with a cliffhanger, which would be annoying.
I imagine a spiritual sequel, maybe even with a direct port / improvement of the smart system, would make more sense. Or, as Rev said, a sequel with a different location but similar story - like what's being done with Bioshock Infinite.